(14ab+3a)(2b2+4a)

To multiply the two polynomials \((14ab + 3a)(2b^2 + 4a)\), we can use the distributive property (also known as the FOIL method for binomials):

\[ (14ab + 3a)(2b^2 + 4a) \]

We'll distribute each term in the first polynomial to each term in the second polynomial:

1. \(14ab \cdot 2b^2 = 28ab^3\)
2. \(14ab \cdot 4a = 56a^2b\)
3. \(3a \cdot 2b^2 = 6ab^2\)
4. \(3a \cdot 4a = 12a^2\)

Now, we combine all these results:

\[ 28ab^3 + 56a^2b + 6ab^2 + 12a^2 \]

Next, let's rearrange the terms in a standard form (typically arranging by the degree of each term):

\[ 28ab^3 + 6ab^2 + 56a^2b + 12a^2 \]

This is the final result of the multiplication. You can further simplify it if needed, but in this case, the expression is in its simplest polynomial form:

\[ 28ab^3 + 6ab^2 + 56a^2b + 12a^2 \]